Finite Group Databasebeta

← #11786402

Subgroups — #11786402

Order 1152.

749 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#208C211yesmaximal, characteristic
2C2×#63657C211yesmaximal, characteristic
3C3×C4×#217C211yesmaximal, characteristic
4C2×Dic3⋊(C3⋊C8)C212yesmaximal, complemented
5#10589155C212yesmaximal, complemented
6#71995—31nomaximal
7#69450—31nomaximal
8C23×C32×C4C2211yescharacteristic
9C22×C3⋊(C3⋊C8)C2211yescharacteristic
10C22×C3⋊(C3⋊C8)C2211yescharacteristic
11C2×C3×#217C412yes—
12C2×C3×C4×Dic3C2212yes—
13C2×C3×#208—22no—
14C2×C3×#208—24no—
15C22×C3×C3⋊C8C2212yes—
16#63657—22no—
17C3×C3⋊#95C411yescharacteristic
18C3×C3⋊#95C411yescharacteristic
19Dic3⋊(C3⋊C8)—24no—
20C22×C3×M16—31no—
21C22×#208D311yescharacteristic
22C3×C4×C22⋊C4—31no—
23C4×#217D311yescharacteristic
24C2×#830—31no—
25C2×#830—31no—
26C2×#830—61no—
27C2×Dic3⋊C8—32no—
28C2×C4⋊(C3⋊C8)—32no—
29#4550—32no—
30#4524—32no—
31C24×C32C2×C411yescharacteristic
32C22×C32×C4—22no—
33C22×C32×C4—22no—
34C22×C32×C4C2×C411yescharacteristic
35C22×C32×C4D412yes—
36C22×C32×C4Q812yes—
37C22×C32×C4C2311yescharacteristic
38C22×C3×Dic3C2×C412yes—
39C22×C3×Dic3C2×C412yes—
40C2×C3⋊(C3⋊C8)—21no—
41C2×C3⋊(C3⋊C8)—21no—
42C2×C3⋊(C3⋊C8)—22no—
43C2×C3⋊(C3⋊C8)—22no—
44C3×#217—24no—
45C3×C4×Dic3—22no—
46C3×C4×Dic3—22no—
47C3×#208—28no—
48C2×C3×C3⋊C8—22no—
49C2×C3×C3⋊C8—22no—
50C2×C3×C3⋊C8D414yes—
51#1851—91noSylow
52C23×C3×C4—21no—
53C23×C3×C4C2×D311yescharacteristic
54C23×C3×C4C2×D311yescharacteristic
55C2×C3×M16—64no—
56C2×C3×M16—62no—
57C22×C3×C8—32no—
58C2×C3×C22⋊C4—32no—
59C2×C3×C42—32no—
60C2×#217Dic312yes—
61C2×C4×Dic3C2×D312yes—
62C2×#208—22no—
63C2×#208—24no—
64C22×C3⋊C8—31no—
65C22×C3⋊C8—31no—
66C22×C3⋊C8—31no—
67C22×C3⋊C8—31no—
68C22×C3⋊C8—61no—
69C22×C3⋊C8—61no—
70C22×C3⋊C8C2×D312yes—
71C3×#95—31no—
72C3×#95—31no—
73C3⋊#95Dic311yescharacteristic
74C3⋊#95Dic311yescharacteristic
75#830—64no—
76#830—62no—
77#830—62no—
78Dic3⋊C8—64no—
79C4⋊(C3⋊C8)—64no—
80C23×C32—21no—
81C23×C32—21no—
82C23×C32—22no—
83C23×C32—22no—
84C23×C32C4⋊C412yes—
85C23×C32C22×C411yescharacteristic
86C2×C32×C4—22no—
87C2×C32×C4—22no—
88C2×C32×C4—24no—
89C2×C32×C4—22no—
90C2×C32×C4C4⋊C412yes—
91C2×C32×C4C2×D411yescharacteristic
92C2×C32×C4C2×D412yes—
93C2×C32×C4C2×Q811yescharacteristic
94C2×C32×C4#4112yes—
95C2×C3×Dic3—22no—
96C2×C3×Dic3—22no—
97C2×C3×Dic3—22no—
98C2×C3×Dic3—22no—
99C2×C3×Dic3—22no—
100C2×C3×Dic3M1614yescomplemented
101C3⋊(C3⋊C8)—41no—
102C3⋊(C3⋊C8)—41no—
103C3×C3⋊C8—24no—
104C22×M16—31no—
105C2×C4⋊C8—92no—
106C2×C22⋊C8—91no—
107C4×C22⋊C4—31no—
108#336—92no—
109C24×C3—21no—
110C24×C3C4×D311yescharacteristic
111C24×C3C2×Dic311yescharacteristic
112C22×C3×C4—22no—
113C22×C3×C4—22no—
114C22×C3×C4—22no—
115C22×C3×C4—22no—
116C22×C3×C4—21no—
117C22×C3×C4—22no—
118C22×C3×C4—22no—
119C22×C3×C4—21no—
120C22×C3×C4—32no—
121C22×C3×C4—32no—
122C22×C3×C4—42no—
123C22×C3×C4—42no—
124C22×C3×C4Dic612yes—
125C22×C3×C4Dic612yes—
126C22×C3×C4C4×D311yescharacteristic
127C22×C3×C4D1212yes—
128C22×C3×C4C2×Dic311yescharacteristic
129C22×C3×C4#6712yes—
130C22×C3×C4C22×D311yescharacteristic
131C22×C3×C4C22×D311yescharacteristic
132C22×Dic3C2×Dic312yes—
133C22×Dic3C2×Dic312yes—
134C3×M16—68no—
135C2×C3×C8—34no—
136C2×C3×C8—62no—
137C2×C3×C8—62no—
138C3×C22⋊C4—64no—
139C3×C42—62no—
140C3×C42—62no—
141#217—24no—
142C4×Dic3—22no—
143C4×Dic3—22no—
144#208—28no—
145C2×C3⋊C8—22no—
146C2×C3⋊C8—22no—
147C2×C3⋊C8—62no—
148C2×C3⋊C8—62no—
149C2×C3⋊C8—61no—
150C2×C3⋊C8—61no—
151C2×C3⋊C8—62no—
152C2×C3⋊C8—62no—
153C2×C3⋊C8—62no—
154C2×C3⋊C8—62no—
155C2×C3⋊C8—61no—
156C2×C3⋊C8—61no—
157C2×C3⋊C8—122no—
158C2×C3⋊C8—122no—
159C2×C3⋊C8#6714yes—
160C22×C32—22no—
161C22×C32—22no—
162C22×C32—22no—
163C22×C32—42no—
164C22×C32—42no—
165C22×C32C2×C4⋊C411yescharacteristic
166C22×C32C4×D412yes—
167C22×C32C2×M1612yes—
168C22×C32#13111yescharacteristic
169C22×C32#13111yescharacteristic
170C32×C4—22no—
171C32×C4#12011yescharacteristic
172C32×C4C22⋊Q812yes—
173C32×C4#12311yescharacteristic
174C3×Dic3—24no—
175C3×Dic3—42no—
176C23×C4D3211yescharacteristic
177C2×M16—64no—
178C2×M16—62no—
179C22×C8—32no—
180C22×C8—91no—
181C22×C8—91no—
182C2×C22⋊C4—32no—
183C2×C42—32no—
184C4⋊C8—184no—
185C22⋊C8—182no—
186#95—31no—
187#95—31no—
188C23×C3—22no—
189C23×C3—22no—
190C23×C3—22no—
191C23×C3—21no—
192C23×C3—21no—
193C23×C3—22no—
194C23×C3—22no—
195C23×C3—22no—
196C23×C3—21no—
197C23×C3—21no—
198C23×C3—22no—
199C23×C3—21no—
200C23×C3—42no—
201C23×C3—42no—
202C23×C3Dic3⋊C412yes—
203C23×C3C4⋊Dic312yes—
204C23×C3C2×C4×D311yescharacteristic
205C23×C3C22×Dic311yescharacteristic
206C2×C3×C4—22no—
207C2×C3×C4—22no—
208C2×C3×C4—24no—
209C2×C3×C4—22no—
210C2×C3×C4—22no—
211C2×C3×C4—24no—
212C2×C3×C4—22no—
213C2×C3×C4—22no—
214C2×C3×C4—22no—
215C2×C3×C4—22no—
216C2×C3×C4—21no—
217C2×C3×C4—21no—
218C2×C3×C4—22no—
219C2×C3×C4—34no—
220C2×C3×C4—44no—
221C2×C3×C4—42no—
222C2×C3×C4—42no—
223C2×C3×C4—42no—
224C2×C3×C4—62no—
225C2×C3×C4—62no—
226C2×C3×C4—62no—
227C2×C3×C4—62no—
228C2×C3×C4—62no—
229C2×C3×C4Dic3⋊C412yes—
230C2×C3×C4C4⋊Dic312yes—
231C2×C3×C4C2×Dic611yescharacteristic
232C2×C3×C4C2×Dic611yescharacteristic
233C2×C3×C4C2×D1211yescharacteristic
234C2×C3×C4#23512yes—
235C2×C3×C4D3×D412yes—
236C2×C3×C4#23712yes—
237C2×C3×C4C2×#6711yescharacteristic
238C2×C3×C4C2×#6712yes—
239C2×Dic3—22no—
240C2×Dic3—22no—
241C2×Dic3—22no—
242C2×Dic3—22no—
243C2×Dic3—22no—
244C2×Dic3#20814yescomplemented
245C3×C8—64no—
246C3⋊C8—24no—
247C3⋊C8—122no—
248C3⋊C8—122no—
249C3⋊C8—121no—
250C3⋊C8—121no—
251C3⋊C8—121no—
252C3⋊C8—121no—
253C2×C32—42no—
254C2×C32#38511yescharacteristic
255C2×C32#42311yescharacteristic
256C2×C32#42411yescharacteristic
257C2×C32#43512yes—
258C2×C32#43612yes—
259C24D3×Dic311yescharacteristic
260C22×C4—22no—
261C22×C4—22no—
262C22×C4—32no—
263C22×C4—32no—
264C22×C4D3×Dic311yescharacteristic
265C22×C4#62612yes—
266C22×C4#62712yes—
267C22×C4C2×D3211yescharacteristic
268M16—68no—
269C2×C8—34no—
270C2×C8—62no—
271C2×C8—62no—
272C2×C8—182no—
273C2×C8—181no—
274C2×C8—181no—
275C2×C8—182no—
276C22⋊C4—64no—
277C42—62no—
278C42—62no—
279C22×C3—24no—
280C22×C3—22no—
281C22×C3—22no—
282C22×C3—22no—
283C22×C3—22no—
284C22×C3—22no—
285C22×C3—22no—
286C22×C3—22no—
287C22×C3—21no—
288C22×C3—21no—
289C22×C3—21no—
290C22×C3—22no—
291C22×C3—42no—
292C22×C3—42no—
293C22×C3—44no—
294C22×C3—44no—
295C22×C3—42no—
296C22×C3—42no—
297C22×C3—42no—
298C22×C3—42no—
299C22×C3D3×M1612yes—
300C22×C3#90711yescharacteristic
301C22×C3#90711yescharacteristic
302C22×C3C2×#20812yes—
303C22×C3C2×Dic3⋊C411yescharacteristic
304C22×C3C2×C4⋊Dic311yescharacteristic
305C22×C3C4×#6712yes—
306C22×C3D4×Dic312yes—
307C22×C3#94811yescharacteristic
308C22×C3#94811yescharacteristic
309C3×C4—22no—
310C3×C4—22no—
311C3×C4—22no—
312C3×C4—21no—
313C3×C4—21no—
314C3×C4—42no—
315C3×C4—64no—
316C3×C4—122no—
317C3×C4#87812yes—
318C3×C4#88211yescharacteristic
319C3×C4#88611yescharacteristic
320C3×C4#92412yes—
321C3×C4#92911yescharacteristic
322C3×C4#95311yescharacteristic
323Dic3—24no—
324Dic3—42no—
325C32#185111yescharacteristic, complemented, Sylow
326C23—22no—
327C23—21no—
328C23—21no—
329C23—22no—
330C23Dic3⋊Dic312yes—
331C23C2×D3×Dic311yescharacteristic
332C2×C4—22no—
333C2×C4—24no—
334C2×C4—22no—
335C2×C4—22no—
336C2×C4—34no—
337C2×C4—62no—
338C2×C4—62no—
339C2×C4—62no—
340C2×C4—62no—
341C2×C4—62no—
342C2×C4Dic3⋊Dic312yes—
343C2×C4#380412yes—
344C2×C4C2×#62611yescharacteristic
345C2×C4C2×#62711yescharacteristic
346C2×C4D3×#6712yes—
347C8—64no—
348C8—361no—
349C8—361no—
350C2×C3—21no—
351C2×C3—21no—
352C2×C3—22no—
353C2×C3—22no—
354C2×C3—21no—
355C2×C3—44no—
356C2×C3—42no—
357C2×C3—42no—
358C2×C3#492411yescharacteristic
359C2×C3#495011yescharacteristic
360C2×C3#499911yescharacteristic
361C2×C3#501112yes—
362C2×C3#501212yes—
363C2×C3#511811yescharacteristic
364C2×C3#511911yescharacteristic
365C2×C3#512712yes—
366C2×C3#512812yes—
367C2×C3#521011yescharacteristic
368C22—22no—
369C22—22no—
370C22—22no—
371C22—42no—
372C22—42no—
373C22D3×#20812yes—
374C22#6381511yescharacteristic
375C22#6381511yescharacteristic
376C22C2×Dic3⋊Dic311yescharacteristic
377C22Dic3×#6712yes—
378C4—22no—
379C4—64no—
380C4—122no—
381C4#6396412yes—
382C4#6396611yescharacteristic
383C4#6397711yescharacteristic
384C3—21no—
385C3#6945011yescharacteristic, complemented
386C3#7199511yescharacteristic, complemented
387C2—42no—
388C2#1059111511yescharacteristic
389C2#1059111711yescharacteristic
390C2#1059114712yes—
391C2#1059115612yes—
392C2#1059171811yescharacteristic
subgroupG/H
center, FrattiniC22×C4C2×D32
commutator, socleC23×C32C22×C4
FittingC23×C32×C4C22
prime radicalC24×C32C2×C4
cosocleC22×C32×C4C23
hypercenterC23×C4D32
hypocenterC32#1851
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C23×C4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
4. C2×Dic3⋊(C3⋊C8)C2semidirect
5. #10589155C2semidirect
100. C2×C3×Dic3M16semidirect
244. C2×Dic3#208semidirect
325. C32#1851semidirect
385. C3#69450semidirect
386. C3#71995semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C22×C3×#2082
C2×#636572
C3×C4×#2172
C2×Dic3⋊(C3⋊C8)2
#105891552
#719953
#694503